What specific blood test can detect reason for hair loss during bath? can headaches have any connection?

No one specific test: One's primary care doctor can check for medical causes. If none are found, then one can see a dermatologist, especially one specializing in hair restoration (some treatments: minoxidil, finasteride, hair transplants, ...). Medical causes may include: hormonal problems (low thyroid), seborrhea, alopecia areata, stressful illness. Other causes: genetic male/female pattern baldness, telogen effluvium